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# Proof question watch

1. how do you prove that

the sum from k=1 to n of k^2

= n(n+1)(2n+1) all over 6??
2. (Original post by Roxanne Knight)
how do you prove that

the sum from k=1 to n of k^2

= n(n+1)(2n+1) all over 6??
Induction
3. yes but how i cant get it to work?!?! lol
4. For a proof by induction:

(1) Show true for a starting point, often n=1 . That's just a check, but vital.

(2) Suppose true for n=k

Then sum from r = 1 to k of r^2 = k(k+1)(2k+1)/6

Consider sum from r = 1 to k+1 of r^2 = k(k+1)(2k+1)/6 + (k+1)^2 I've just added one term to series

Then work out the algebra
Show that the result agrees with the supposed formula but with (k+1) replacing each k

So true for n= k+1

So proved by induction

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Updated: February 2, 2010
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